Transcript Management of Financial Risk

Financial Risk Management
Zvi Wiener
Following
P. Jorion, Financial Risk Manager Handbook
http://pluto.huji.ac.il/~mswiener/zvi.html
FRM
972-2-588-3049
Chapter 13
Sources of Risk
Following P. Jorion 2001
Financial Risk Manager Handbook
http://pluto.huji.ac.il/~mswiener/zvi.html
FRM
972-2-588-3049
Currency Risk
• free movements of currency
• devaluation of a fixed or pegged currency
• regime change (Israel, Europe)
Ch. 13, Handbook
Zvi Wiener
slide 3
Currency Volatility
Argentina
Australia
Canada
Switzerland
Denmark
Britain
Hong Kong
Indonesia
Japan
Korea
Ch. 13, Handbook
End 99
0.35
7.6
5.1
10
9.8
6.5
0.3
24
11
6.9
Zvi Wiener
End 96
0.4
8.5
3.6
10
7.8
9.1
0.3
1.6
6.6
4.5
slide 4
Currency Volatility
Mexico
Malaysia
Norway
New Zealand
Philippines
Sweden
Singapore
Thailand
Taiwan
Euro
S. Africa
Ch. 13, Handbook
End 99
7.5
0.1
7.6
13.4
5.5
8.5
3.8
9.7
1.8
9.8
4.2
Zvi Wiener
End 96
7
1.6
7.6
7.9
0.6
6.4
1.8
1.2
0.9
8.3
8.4
slide 5
FRM-97, Question 10
Which currency pair would you expect to have
the lowest volatility?
A. USD/DEM
B. USD/CAD
C. USD/JPY
D. USD/ITL
Ch. 13, Handbook
Zvi Wiener
slide 6
FRM-97, Question 10
Which currency pair would you expect to have
the lowest volatility?
A. USD/DEM
B. USD/CAD
C. USD/JPY
D. USD/ITL
Ch. 13, Handbook
Zvi Wiener
slide 7
FRM-97, Question 14
What is the implied correlation between
JPY/DEM and DEM/USD when given the
following volatilities for foreign exchange rates?
JPY/USD 8%, JPY/DEM 10%, DEM/USD 6%
A. 60%
B. 30%
C. -30%
D. -60%
Ch. 13, Handbook
Zvi Wiener
slide 8
Cross Rate volatility
JPY/USD = x
x
y
z
JPY/DEM = y
x  yz
DEM/USD = z
ln x  ln y  ln z
 (ln x)   (ln y)   (ln z)  2ln y ln z (ln y) (ln z)
2
2
2
0.08  0.1  0.06  2  0.1 0.06
2
2
2
0.01  0.0036  0.0064
0.0072
 

 0.6
2  0.06  0.1
0.012
Ch. 13, Handbook
Zvi Wiener
slide 9
Fixed Income Risk
Arises from potential movements in the level
and volatility of bond yields.
Factors affecting yields
• inflationary expectations
• term spread
• higher volatility of the low end of TS
Ch. 13, Handbook
Zvi Wiener
slide 10
Volatilities of IR/bond prices
Price volatility in %
Euro 30d
Euro 180d
Euro 360d
Swap 2Y
Swap 5Y
Swap 10Y
Zero 2Y
Zero 5Y
Zero 10Y
Zero 30Y
Ch. 13, Handbook
End 99
0.22
0.30
0.52
1.57
4.23
8.47
1.55
4.07
7.76
20.75
Zvi Wiener
End 96
0.05
0.19
0.58
1.57
4.70
9.82
1.64
4.67
9.31
23.53
slide 11
Duration approximation
 P 

  D * (y)
 P 
What duration makes bond as volatile as FX?
What duration makes bond as volatile as stocks?
A 10 year bond has yearly price volatility of 8%
which is similar to major FX.
30-year bonds have volatility similar to equities
(20%).
Ch. 13, Handbook
Zvi Wiener
slide 12
Models of IR
Normal model (y) is normally distributed.
Lognormal model (y/y) is normally distributed.
Note that:
Ch. 13, Handbook
 y 
 (y)  y    
 y 
Zvi Wiener
slide 13
Time adjustment
Square root of time adjustment is more
questionable for bond prices than for other
assets
• there is a strong evidence of mean reversion
• bond prices converge approaching maturity
(bridge effect) - strong for short bonds, weak for
long.
Ch. 13, Handbook
Zvi Wiener
slide 14
Volatilities of yields
Yield volatility in %, 99 (y/y)
Euro 30d
45
Euro 180d
10
Euro 360d
9
Swap 2Y
12.5
Swap 5Y
13
Swap 10Y
12.5
Zero 2Y
13.4
Zero 5Y
13.9
Zero 10Y
13.1
Zero 30Y
11.3
Ch. 13, Handbook
Zvi Wiener
(y)
2.5
0.62
0.57
0.86
0.92
0.91
0.84
0.89
0.85
0.74
slide 15
FRM-99, Question 86
For computing the market risk of a US T-bond
portfolio it is easiest to measure:
A. yield volatility, because yields have positive
skewness.
B. price volatility, because bond prices are
positively correlated.
C. yield volatility for bonds sold at a discount
and price volatility for bonds sold at a premium.
D. yield volatility because it remains more
constant over time than price volatility, which
must approach zero at maturity.
Ch. 13, Handbook
Zvi Wiener
slide 16
FRM-99, Question 86
For computing the market risk of a US T-bond
portfolio it is easiest to measure:
A. yield volatility, because yields have positive
skewness.
B. price volatility, because bond prices are
positively correlated.
C. yield volatility for bonds sold at a discount
and price volatility for bonds sold at a premium.
D. yield volatility because it remains more
constant over time than price volatility, which
must approach zero at maturity.
Ch. 13, Handbook
Zvi Wiener
slide 17
FRM-99, Question 80
You have position of $20M in the 6.375% Aug-27
US T-bond. Calculate daily VaR at 95% assume
that there are 250 business days in a year.
Price 98 8/32
Accrued 1.43%
Yield 6.509%
Duration 13.133
Modified Dur. 12.719 Yield volatility 12%
A. $291,400
B. $203,080
C. $206,036
D. $206,698
Ch. 13, Handbook
Zvi Wiener
slide 18
FRM-99, Question 80
Value of the position
8

 1
$20 98   1.43
 $19.936
32

 100
Daily yield volatility
 y  1
 (y)  y   annual  
 0.000494
 y  250
VaR  D *P 1.645  (y)
VaR  12.719 $19.936M 1.645 0.000494 $206,055
Ch. 13, Handbook
Zvi Wiener
slide 19
Correlations
Eurodeposit block
zero-coupon Treasury block
very high correlations within each block and
much lower across blocks.
Ch. 13, Handbook
Zvi Wiener
slide 20
Principal component analysis
• level risk factor 94% of changes
• slope risk factor (twist) 4% of changes
• curvature (bend or butterfly)
See book by Golub and Tilman.
Ch. 13, Handbook
Zvi Wiener
slide 21
FRM-00, Question 96
Which statement about historic US Treasuries
yield curves is TRUE?
Ch. 13, Handbook
Zvi Wiener
slide 22
FRM-00, Question 96
A. Changes in the long-term yield tend to be
larger than in short-term yield.
B. Changes in the long-term yield tend to be
approximately the same as in short-term yield.
C. The same size yield change in both long-term
and short-term rates tends to produce a larger
price change in short-term instruments when all
securities are traded near par.
D. The largest part of total return variability of
spot rates is due to parallel changes with a smaller
portion due to slope changes and the residual due
to curvature changes.
Ch. 13, Handbook
Zvi Wiener
slide 23
FRM-00, Question 96
A. Changes in the long-term yield tend to be
larger than in short-term yield.
B. Changes in the long-term yield tend to be
approximately the same as in short-term yield.
C. The same size yield change in both long-term
and short-term rates tends to produce a larger
price change in short-term instruments when all
securities are traded near par.
D. The largest part of total return variability of
spot rates is due to parallel changes with a smaller
portion due to slope changes and the residual due
to curvature changes.
Ch. 13, Handbook
Zvi Wiener
slide 24
FRM-97, Question 42
What is the relationship between yield on the
current inflation-proof bond issued by the US
Treasury and a standard Treasury bond with
similar terms?
A. The yields should be about the same.
B. The yield on the inflation protected bond
should be approximately the yield on treasury
minus the real interest.
C. The yield on the inflation protected bond
should be approximately the yield on treasury plus
the real interest.
D. None of the above.
Ch. 13, Handbook
Zvi Wiener
slide 25
• Credit Spread Risk
• Prepayment Risk (MBS and CMO)
• seasoning
• current level of interest rates
• burnout (previous path)
• economic activity
• seasonal patterns
• OAS = option adjusted spread = spread over
equivalent Treasury minus the cost of the
option component.
Ch. 13, Handbook
Zvi Wiener
slide 26
FRM-99, Question 71
You held mortgage interest only (IO) strips backed by
Fannie Mae 7 percent coupon. You want to hedge this
by shorting Treasury interest strips off the 10-year
on-the-run. The curve steepens as 1 month rate drops,
while the 6 months to 10 year rates remain stable.
What will be the effect on the value of your
portfolio?
A. Both IO and the hedge appreciate in value.
B. Almost no change in both (may be a small
appreciation).
C. Not enough information to find changes in both.
D. The IO will depreciate, the hedge will appreciate.
Ch. 13, Handbook
Zvi Wiener
slide 27
FRM-99, Question 71
You held mortgage interest only (IO) strips backed by
Fannie Mae 7 percent coupon. You want to hedge this
by shorting Treasury interest strips off the 10-year
on-the-run. The curve steepens as 1 month rate drops,
while the 6 months to 10 year rates remain stable.
What will be the effect on the value of your
portfolio?
A. Both IO and the hedge appreciate in value.
B. Almost no change in both (may be a small
appreciation).
C. Not enough information to find changes in both.
D. The IO will depreciate, the hedge will appreciate.
Ch. 13, Handbook
Zvi Wiener
slide 28
FRM-99, Question 73
A fund manager attempting to beat his LIBOR
based funding costs, holds pools of adjustable
rate mortgages and is considering various
strategies to lower the risk. Which of the
following strategies will NOT lower the risk?
A. Enter a total rate of return swap swapping
the ARMs for LIBOR plus a spread.
B. Short US government bonds
C. Sell caps based on the projected rate of
mortgage paydown.
D. All of the above.
Ch. 13, Handbook
Zvi Wiener
slide 29
FRM-99, Question 73
A fund manager attempting to beat his LIBOR
based funding costs, holds pools of adjustable
rate mortgages and is considering various
strategies to lower the risk. Which of the
following strategies will NOT lower the risk?
A. Enter a total rate of return swap swapping
the ARMs for LIBOR plus a spread.
B. Short US government bonds.
C. Sell caps based on the projected rate of
mortgage paydown. He should buy caps, not sell!
D. All of the above.
Ch. 13, Handbook
Zvi Wiener
slide 30
Fixed income portfolio risk
• Yield curve component (government)
• Credit spread (of the class of similar rating)
• Specific spread
Ch. 13, Handbook
Zvi Wiener
slide 31
Equity risk
• Market risk (beta based relative to an index)
• Specific risk
Ch. 13, Handbook
Zvi Wiener
slide 32
FRM-97, Question 43
Which of the following statements about SP500 is
true?
I. The index is calculated using market prices as
weights.
II. The implied volatilities of options of the same
maturity on the index are different.
III. The stocks used in calculating the index remain
the same for each year.
IV. The SP500 represents only the 500 largest US
corporations.
A. II only.
B. I and II.
C. II and III.
D. III and IV only.
Ch. 13, Handbook
Zvi Wiener
slide 33
FRM-97, Question 43
Which of the following statements about SP500 is
values
true?
I. The index is calculated using market prices as
weights.
II. The implied volatilities of options of the same
maturity on the index are different.
III. The stocks used in calculating the index remain
the same for each year.
IV. The SP500 represents only the 500 largest US
corporations.
A. II only.
B. I and II.
C. II and III.
D. III and IV only.
Ch. 13, Handbook
Zvi Wiener
slide 34
Forwards and Futures
Ft e
 rt
 St e
 yt
The forward or futures price on a stock.
e-rt the present value in the base currency.
e-yt the cost of carry (dividend rate).
For a discrete dividend (individual stock) we
can write the right hand side as St- D, where D
is the PV of the dividend.
Ch. 13, Handbook
Zvi Wiener
slide 35
FRM-97, Question 44
A trader runs a cash and future arbitrage book
on the SP500 index. Which of the following
are the major risk factors?
I. Interest rate
II. Foreign exchange
III. Equity price
IV. Dividend assumption risk
A. I and II only.
B. I and III only.
C. I, III, and IV only.
D. I, II, III, and IV.
Ch. 13, Handbook
Zvi Wiener
slide 36
FRM-97, Question 44
A trader runs a cash and future arbitrage book
on the SP500 index. Which of the following
are the major risk factors?
I. Interest rate
II. Foreign exchange
III. Equity price
IV. Dividend assumption risk
A. I and II only.
B. I and III only.
C. I, III, and IV only.
D. I, II, III, and IV.
Ch. 13, Handbook
Zvi Wiener
slide 37
CAPM
Ri  i  i  RM   i
i 
Cov( Ri , RM )

2
M
 i,M
 ( Ri )
 ( RM )
In an equilibrium the following holds (Sharpe)
ERi   R f  i ERM   R f 
Ch. 13, Handbook
Zvi Wiener
slide 38
APT
Arbitrage Pricing Theory
Ri  i  i1  y1  iK  yK   i
Ch. 13, Handbook
Zvi Wiener
slide 39
FRM-98, Question 62
In comparing CAPM and APT, which of the
following advantages does APT have over
CAPM?
I. APT makes less restrictive assumptions about
investor preferences toward risk and return.
II. APT makes no assumption about the
distribution of security returns.
III. APT does not rely on the identification of
the true market portfolio, and so the theory is
potentially testable.
A. I only.
B. II and III only.
C. I, and III only.
D. I, II, and III.
Ch. 13, Handbook
Zvi Wiener
slide 40
FRM-98, Question 62
In comparing CAPM and APT, which of the
following advantages does APT have over
CAPM?
I. APT makes less restrictive assumptions about
investor preferences toward risk and return.
II. APT makes no assumption about the
distribution of security returns.
III. APT does not rely on the identification of
the true market portfolio, and so the theory is
potentially testable.
A. I only.
B. II and III only.
C. I, and III only.
D. I, II, and III.
Ch. 13, Handbook
Zvi Wiener
slide 41
Commodity Risk
Base metal - aluminum, copper, nickel, zinc.
Precious metals - gold, silver, platinum.
Energy products - natural gas, heating oil,
unleaded gasoline, crude oil.
Metals have 12-25% yearly volatility.
Energy products have 30-100% yearly
volatility (much less storable).
Long forward prices are less volatile then
short forward prices.
Ch. 13, Handbook
Zvi Wiener
slide 42
FRM-97, Question 12
Which of the following products should have the
highest expected volatility?
A. Crude oil
B. Gold
C. Japanese Treasury Bills
D. DEM/CHF
Ch. 13, Handbook
Zvi Wiener
slide 43
FRM-97, Question 12
Which of the following products should have the
highest expected volatility?
A. Crude oil
B. Gold
C. Japanese Treasury Bills
D. DEM/CHF
Ch. 13, Handbook
Zvi Wiener
slide 44
FRM-97, Question 23
Identify the major risks of being short $50M of
gold two weeks forward and being long $50M of
gold one year forward.
I. Spot liquidity squeeze.
II. Spot risk.
III. Gold lease rate risk.
IV. USD interest rate risk.
A. II only.
B. I, II, and III only.
C. I, III, and IV only.
D. I, II, III, and IV.
Ch. 13, Handbook
Zvi Wiener
slide 45
FRM-97, Question 23
Identify the major risks of being short $50M of
gold two weeks forward and being long $50M of
gold one year forward.
I. Spot liquidity squeeze.
Spot risk is eliminated
II. Spot risk.
by offsetting positions
III. Gold lease rate risk.
IV. USD interest rate risk.
A. II only.
B. I, II, and III only.
C. I, III, and IV only.
D. I, II, III, and IV.
Ch. 13, Handbook
Zvi Wiener
slide 46